Refractivity retrieval via direct measurement of GNSS bending angle

ABSTRACT

A method and system for taking direct measurements of GNSS signal&#39;s arrival angle to remotely measure the atmospheric variables used for weather prediction. More specifically, an improved method and system for obtaining and processing accurate information regarding the weather and other atmospheric changes by measuring the total refractive bending angle of the GNSS signal. For mobile platforms on which receivers are mounted, phased array receivers are used to allow precise measurements of GNSS arrival angles. By measuring the refractive bending angle, more accurate and cost-efficient measurements of atmospheric changes are obtained, thereby resulting in more accurate predictions of the weather.

BACKGROUND OF THE INVENTION

The present invention relates generally to a method for remotelymeasuring the atmospheric variables used for weather prediction and moreparticularly to a method for estimating the refractivity profile of theEarth's atmosphere.

Measurements of satellite systems such as Global Navigation SatelliteSystems (GNSS) are generally accurate, however, they operate onfrequencies that are sensitive to atmospheric effects. Similarsatellite-based navigation systems such as GLONASS and GALILEO are alsosensitive to atmospheric effects. To enable the GNSS systems to detectany changes in atmospheric properties or any slight change in refractionof the signals due to natural variations in the atmosphere, sensitivereceivers must be used. Currently GNSS systems rely on phase shiftingcalculations to measure atmospheric properties. To produce weatherpredictions and forecasts, the GNSS systems measure the excess phaseshift induced by the GNSS signals following a refracted path through theatmosphere to a GNSS receiver, rather than the straight path the GNSSsignal would follow if there were no change in the atmosphericproperties. As the GNSS satellites rise or set, the length of the paththat the GNSS signals travel through the atmosphere varies due torefraction. The amount of refraction varies based on how much changethere is in the atmospheric properties. Also, as the signal path lengthand atmosphere refractivity vary, the phase shift of the GNSS signalschange as well. Currently, in order to generate refractivity profilesfrom phase measurements taken along various lines of sight, variousalgorithms are used with data gathered through phase shiftingmeasurements. Most methods currently measure phase shift directly, whichrequires advance knowledge of the location of the receiving antenna.When the receiving antenna is carried on a moving platform such as anaircraft, determining the precise location of the antenna makescalculating the phase shift even more difficult.

Another current system for weather prediction measures atmosphericchanges using measurements of excess Doppler shift versus time, and thenuses these measurements to estimate the phase shift. This methodrequires less knowledge of the precise location of the antennas andreceivers; however, it has yet to be initiated in real-worldapplications. All of the prior and current solutions for measuringatmospheric refractivity changes to predict weather forecasts aregenerally characterized by having poor signal-to-noise ratios. Becauseof the poor signal to noise ratios, the excess phase shift caused by anychanges in temperature or humidity approaches the resolution limit foreven advanced GNSS receivers. GNSS receivers that are in motion,including the receivers moving on non-ballistic paths, are especiallyaffected by poor signal-to-noise ratios. Even the Doppler shift versustime approach has a similar problem with the poor signal-to-noise ratio.The excess Doppler shift due to temperature or humidity variations inthe atmosphere is close to the frequency resolution limit for receiverson mobile platforms.

Another deficiency with the current systems is that they operate as ifthe atmosphere is horizontally homogeneous. While incorrect, thisassumption is required for the refractivity profile algorithms used inthese systems. While the assumption of a horizontally homogeneousatmosphere is the best solution for this system, it leads to errors inrefractivity estimates and degrades the horizontal resolution ofoccultation measurements, thereby creating errors in weather predictionbased on these methods.

Thus, there is a need for a method and system to accurately measurerefraction of GNSS signals caused by changes in the Earth's atmosphere.With such a system, more accurate GNSS measurements can be recorded, andfurther, more accurate weather predictions will result.

SUMMARY OF INVENTION

The present invention is directed to a method of determiningrefractivity properties of the Earth's atmosphere using GlobalNavigation Satellite System (GNSS) signals. The method includes thesteps of providing a plurality of antenna elements configured to measurethe arrival angle of a GNSS signal, mounted on a platform and separatedby a predetermined vertical distance, and one receiver device, which isconnected to each of the antenna elements; receiving the GNSS signal ateach of the plurality of antenna elements; measuring an arrival angle bymeasuring a phase of the GNSS signal for each of the plurality ofantenna elements; determining a difference between the nominal arrivalangle of the GNSS signal and the measured arrival angle of the GNSSsignal; calculating a refractive bending angle between measured andnominal GNSS arrival angles; and transforming the refractive bendingangle of the GNSS signal into profiles of physical properties of theatmosphere.

Another aspect of the invention is directed to a method of determiningrefractivity properties of the Earth's atmosphere using GlobalNavigation Satellite System (GNSS) signals. The method includes thesteps of providing a plurality of antenna elements configured to measurean actual arrival angle and actual arrival phase of a GNSS signal,mounted on a platform and separated by a predetermined verticaldistance, and one receiver device, which is coupled to each of theplurality of antenna elements and configured to calculate a nominalarrival angle and a nominal arrival phase of the GNSS signal based ondata transmitted from a source of the GNSS signal. The method alsoincludes receiving the GNSS signal at each of the plurality of antennaelements, measuring an actual arrival angle of the GNSS signal andmeasuring an actual arrival phase of the GNSS signal for each antennaelement of the plurality of antenna elements. In addition, the methoddetermines a difference between the nominal arrival angle of the GNSSsignal and the actual arrival angle of GNSS signal, determines adifference between the nominal arrival phase of the GNSS signal and theactual arrival phase of GNSS signal and calculates a refractive bendingangle and an absolute phase shift of the GNSS signal based on thedetermined differences between the actual and nominal arrival angles ofthe GNSS signal and the actual and nominal arrival phases of the GNSSsignal. Lastly, the method involves generating a profile of physicalproperties of the atmosphere based on a transformation of the refractivebending angle of the GNSS signal and the absolute phase shift of theGNSS signal.

In yet another aspect of the present invention, there is a system fordetermining refractivity properties of the Earth's atmosphere usingGlobal Navigation Satellite System (GNSS) signals. The system includes aplurality of antenna elements configured to measure the arrival angle ofa GNSS signal, mounted on a platform and separated by a predeterminedvertical distance and a receiver unit coupled to each of the pluralityof antenna elements. The receiver unit is configured to receive the GNSSsignal detected by each of the plurality of antenna elements, measure anactual arrival phase of the GNSS signal for each antenna element andcompute an actual arrival angle from the arrival phase. In addition, thereceiver unit is configured to determine a difference between thenominal arrival angle of the GNSS signal and the actual arrival angle ofGNSS signal, determine a difference between the nominal arrival phase ofthe GNSS signal and the actual arrival phase of GNSS signal, calculate arefractive bending angle and an absolute phase shift of the GNSS signalbased on the determined differences between the actual and nominalarrival angles of the GNSS signal and the actual and nominal arrivalphases of the GNSS signal and lastly, generate a profile of physicalproperties of the atmosphere based on a transformation of the refractivebending angle of the GNSS signal and the absolute phase shift of theGNSS signal.

Rather than inferring the bending angles from the total phase shift ofthe signals as in the current systems, the present invention directlymeasures the total angle of refraction of the signal. The directmeasurement of the total angle of refraction at the receiver results ina more accurate measurement of the changes in atmospheric propertiesused in weather prediction models.

Errors in the relative phase between two nearby antenna elements arelargely independent of errors in absolute phase for the pair of antennaelements. Statistical measurements with independent errors can becombined to reduce the overall error, therefore, improved noisereduction and precision in the GNSS signal detection process occurs whenthe direct measurement of the angle of refraction of the signal iscombined with ordinary GNSS signal phase shift occultation.

One advantage of the present invention is that a more direct measurementof refractive bending of GNSS signals in the Earth's atmosphere isobtained.

Another advantage of the present invention is the improvement of noisereduction and precision in the GNSS signal detection.

Yet another advantage of the present invention is the reduction in thetotal error of the refractivity profile.

Another advantage of the present invention is the mitigation ofambiguity in other factors such as location, size, and the refractivityof atmospheric features affecting the incoming signals to the receivers.The potential errors for these factors are corrected in the presentinvention by using measurements of the refractive bending angle combinedwith measurements of absolute phase angle of the signal.

Other features and advantages of the present invention will be apparentfrom the following more detailed description of the preferredembodiment, taken in conjunction with the accompanying drawings whichillustrate, by way of example, the principles of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a global system for the detection of clear airatmospheric changes in accordance with the principles of the presentinvention.

FIG. 2 illustrates the preferred embodiment of the vertical phased arrayGNSS antenna elements.

FIG. 3 illustrates the directional angled paths of the GNSS signalrefractivity.

FIG. 4 illustrates the directional angled paths of the GNSS signalrefractivity in terms of the receiver's distance from the transmitter.

FIG. 5A illustrates an alternate embodiment of the invention including athird antenna element from the top view.

FIG. 5B illustrates an alternate embodiment of the invention including athird antenna element from the side view.

FIG. 5C illustrates the directional angled paths of the GNSS signalaffected by a horizontal refractivity gradient.

FIGS. 6, 8 and 9 are flow diagrams of the method of the presentinvention.

FIGS. 7 and 9 are flow diagrams of an alternative embodiment of a methodof the present invention.

Wherever possible, the same reference numbers will be used throughoutthe drawings to refer to the same or like parts.

DETAILED DESCRIPTION OF THE INVENTION

Many modern aircraft use radio-positioning signals broadcast fromsatellites (e.g. GPS, GLONASS, GALILEO) for navigation. It is to beunderstood that while the term GNSS is used throughout the detaileddescription of the invention, any one of the available satellite systemsmay be used with the present invention. While any one signal onlyconveys information regarding the changes in atmospheric propertiesalong its own path, the large number of GNSS receivers and satellitescurrently in use provide a plethora of measurements of atmosphericproperties along the numerous paths between these devices. By collectingdata and information from all of these signals, more accurate weatherprediction forecasts and models can be produced.

It has been shown that the index of refraction is related to theproperties of air as follows:(n−1)×10⁶ =a ₁ P/T+a ₂ P _(w) /T ²  Equation 1

where:

-   -   n=index of refraction    -   T=Air Temperature    -   P=Air Pressure    -   P_(W)=Water Vapor Pressure    -   a₁=77.6 K mbar⁻¹    -   a₂=3.73×10⁵ K2 mbar⁻¹        Ao, C. O. et al., Lower-Troposphere Refractivity Bias in GPS        Occultation Retrievals, Journal of Geophysical Research, 108        (D18), Pages 1-12.

As a result, the air refracts electromagnetic waves as the waves passthrough it. The amount of refraction occurring along a wave's (orsignal's) path therefore changes as the path changes. The changingamount of refraction causes several measurable alterations to thesignal. More particularly, these alterations include changes in thephase, the intensity, and the frequency of the wave induced by changesto the path that the signal travels.

The exemplary system 10 shown in FIG. 1 includes a constellation ofsatellites 12, 14, 16, 18 and 20, a plurality of mobile platforms 22, 24and 26, and a ground station 28 distributed in such a manner as todetect the changes in atmospheric properties 30 that might occur. Whilethe change in atmospheric properties 30 is shown as a cumulonimbus cloud(i.e., a thunderstorm) it will be understood that the principles of thepresent invention apply equally to any changes in atmospheric propertiesthat may occur, including atmospheric changes that bear no visibleindication.

The satellites 12, 14, 16, 18 and 20 may be any satellite that transmitssignals in the form of electromagnetic energy (e.g., radio frequencyenergy) generally towards the Earth or any other celestial body havingan atmosphere. Preferably, the satellites are components of aconstellation of satellites such as a system for providing globalpositioning services (e.g., GPS, GLONASS, or GALILEO systems), a systemfor providing telecommunications (e.g., Iridium, Globalstart,Intermediate Circuilar Orbit, Orbcomm, or Teledesic systems), or even acollection of unrelated satellites. Likewise, the particular mobileplatforms 22, 24 and 26 used are not critical. But exemplary mobileplatforms include aircraft 22 and 24 and ships 26 as well as other air,space, marine, and land vehicles. Preferably, each satellite 12, 14, 16,18 and 20 carries a transmitter to broadcast signals for receipt byreceivers at the terrestrial portions 22, 24, 26 and 28 of the system 10although the location of the receivers and transmitters can be reversedor interchanged without departing from the scope of the presentinvention.

The transmission of the signals between the transmitters and receiversis illustrated by a variety of signal paths in FIG. 1. For instance,satellite 12 is shown transmitting two signals received by the aircraft22 and one signal received by the ship 26 via, respective paths 36, 38and path 40. Satellite 14 is also shown transmitting to the aircraft 22via path 42. Likewise, satellite 16 is transmitting to the aircraft 24via path 44 and satellite 18 is transmitting to the ship 26 via path 46.As is apparent from FIG. 1, each of the receiving portions andtransmitting portions respectively of the system 10 can receive ortransmit a single signal or multiple signals.

The majority of these paths 36, 38, 40, 42, 44 and 46 will pass throughthe atmosphere 32 while being altered by conditions in the atmosphere.These alterations will typically include phase shifts, frequency shifts,and intensity changes in the signal as it is received at the terrestrialportions 22, 24, 26 and 28 of the system 10. Also worth noting is thatmany portions of the system 10 move. Thus, the paths 36, 38, 40, 42, 44and 46 will sweep through the atmosphere forming curvilinearthree-dimensional surfaces along which the signals travel during thetime that any pair of transmitters and receivers are visible to one andanother. As the mobile components of the system 10 move, the paths willencounter varying degrees of atmospheric properties 30. For example,paths 36, 38, 40 and 24 are shown traversing relatively dry or clearportions of the atmosphere while paths 42 and 46 are both shownpenetrating the volume of moist air 30 albeit at different locations andangles. Thus, changes in atmospheric properties 30 can alter the signalstraveling on the paths 42 and 46 to a greater extent than the atmospherealters the signals traveling on the other paths 36, 38, 40, and 44.

Referring to FIG. 2, the present invention uses measurements of thenominal arrival angle 48 of the GNSS signal to determine the totalrefraction of the GNSS signal due to the atmospheric conditions. Thenominal arrival angle 48 (α₀) is the elevation angle of a straight linefrom a GNSS satellite 12, 14, 16, 18, 20 arriving at a terrestrialportion 22, 24, 26, 28 of the system. The nominal arrival angle 48 iscomputed from known positions of the satellites 14 and the antennaelements 50, 52. The satellite positions are calculated from informationencoded in the GNSS signal. For non-GNSS satellites, the position iscalculated from published ephemerises. The antenna element positions arefound in any one of several ways, one way being using GNSS informationfrom multiple satellites. The calculation of the nominal arrival angle48 and the direct measurement of the actual arrival angle 56 reveals thetotal refractive bending caused by the path of the signal through theatmosphere and any atmospheric properties 30 that the GNSS signal mayencounter along the path. To enable the direct measurement of therefractive bending angle, phased array receivers 54 are used to obtainprecise measurements of the GNSS arrival angles. The absolute arrivalangle is the angle relative to geographically fixed coordinates, e.g.earth-centered coordinates. Both the actual arrival angle 56 (α₁) andthe nominal arrival angle 48 can be measured as an absolute angle. Theabsolute arrival angle is obtained by measuring the absolute orientationof the antenna, and then adding the arrival angle relative to theantenna axes. Subtracting the absolute arrival angle from the absolutenominal arrival angle will result in a measurement for one type ofrelative arrival angle. An alternative arrival angle is the angle of thesignal relative to the axes of the antenna.

The present invention uses a vertical phased array of two or more GNSSantenna elements 50, 52. The use of two antenna elements 50, 52 providesfor more accurate measurements of the refractive angle of the signals.Vertical separation between the antenna elements 50, 52 must be greatenough to allow the angle measurements to detect a 1% variation in totalGNSS refracting angle at the surface of the Earth. The typical totalrefractive angle for the atmosphere of the Earth is about 1.42 degrees,which is the same regardless of the GNSS system used. Therefore, theactual arrival angle 56 must be measured within 0.014 degrees, or2.49×10⁻⁴ radian of the actual value of the arrival angle. The actualarrival angle 56 is calculated from the refractive bending angle 58between the two antenna elements 50, 52 on the vertical surface 60, orplatform. GNSS phase difference between two antennas 50, 52 can bemeasured to better than 0.01 wavelength, i.e. about 2 millimeters. Inorder to obtain the required angular precision, the antenna elements 50,52 must have a vertical separation 62 (Δ_(Z)) that is typical for theatmosphere of the Earth. The vertical separation 62 is dependent uponthe wavelength of the signal, where the wavelength varies with eachsatellite used. The value for vertical separation used for the presentinvention is calculated for a GPS GNSS satellite system, since GPS isused by a vast majority of all aircraft. The required verticalseparation 62 must be at least as large as the value calculated by:Δ_(Z)=Δ_(φ)/Δ_(α)  Equation 2

where:

-   -   Δ_(φ)=the phase difference in the phases of the nominal arrival        angle α₀ and the actual arrival angle α₁    -   Δ_(α)=the difference between the nominal arrival angle α₀ and        the actual arrival angle α₁        Δ_(Z)=2×10⁻³ meters/2.49×10⁻⁴ radian Δ_(Z)=8.03 meters

While the platform 60 is shown as a planar or linear surface in FIG. 2,it should be noted that this is a schematic illustration, and that thevertical separation 62, of 8.03 meters can be achieved on verticalmobile surfaces 60 or platforms, e.g. ships, buildings, or largetransport airplanes. For platforms 26 that are stationary, e.g.buildings, or that have less movement than mobile platforms 22, thevertical separation 62 is simple to achieve due to their wide girth andlarge surface area. On highly mobile platforms 22, e.g. airplanes, thevertical separation 62 between the antenna elements 50, 52 maybeachieved by affixing one antenna 52 on the fuselage and one antenna 50on the top of the vertical tail on a typical airliner, or even fromlocations on the upper and lower fuselage for larger, wider bodiedairliners.

In an alternate embodiment, the present invention may be implemented byhaving at least one high-gain steerable dish antenna element in thephased array GNSS unit antenna elements. This alternate arrangement maybe preferable in situations where the high-gain steerable dish antennaelements are already installed and available, thereby avoiding the costof installation of phased array GNSS antenna elements and receivers.

The present invention is used to make the physical measurements of anychanges in atmospheric properties to enable reliable predictions of theweather and to produce more accurate weather forecasts. When theequipment shown in FIG. 2 is mounted on mobile platforms 22, e.g.airplanes, the invention may include inertial measurement units (IMUs)or other means to estimate relative motion of the various GNSS antennaelements (e.g. star tracker, horizon tracker, or a DGPS usinghigh-elevation satellites). The use of IMUs assists in reducing error inangle measurements by subtracting the relative phase shifts due tostructural motion from the measured phase shifts. The remaining phaseshifts after subtracting relative phase shifts due to structural motionare due to the arrival angle. The use of an IMU allows the invention tocompensate for motion and rotation of the vehicle. The use of multipleIMUs, preferably one near each antenna element 50, 52, allows theinvention to compensate for any flexing of the structure.

Ambiguity can occur when dealing with horizontal homogeneity. Forsimplicity, only GNSS signal 44 (FIG. 1) will be used for the followingexplanation, with the understanding that any of the GNSS signals can beused. The Earth's atmosphere is not horizontally uniform, although manymeasurements and calculations assume a horizontally uniform atmosphere.Because of the assumption, a homogeneous model introduces error byforcing a refractivity profile to calculate accurate results with aninaccurate factor. Therefore, to reduce this error, measurements of therefractive angle of the phased array GNSS signal 44 are combined withmeasurements of absolute phase of the phased array GNSS signal 44 formore accurate measurements with no assumption of horizontal homogeneity.The combination of the refractive angle and the absolute phase of theGNSS signal 44 results in a reduction of the ambiguity of elements suchas location, size, and refractivity of atmospheric features, e.g.reportable weather-related changes in atmosphere properties.

Referring to FIG. 3, a comparison of two GNSS signal paths 96, 98illustrates how ambiguity due to vertical non-homogeneity can affect theabsolute phase angle of the GNSS signal 44. The GNSS signal 44 traversesconvex regions having high refractivity values N₀ and N₁, i.e., theregions are non-homogeneous. In the example of FIG. 3, GNSS pathtraverses a first region 91 characterized by a first refractivity valueN₀, and through a second region 90 characterized by a secondrefractivity value, N₁, to reach aircraft A as GNSS signal path 97. Thesecond region 90 is large, but distant from aircraft A. In the case ofaircraft B, however, the GNSS path 44 similarly traverses regions 93 and94. Regions 93 and 94 have different refractivity values. Region 94 issmaller than region 90, and has a refractivity value of 2N₁, or twicethe refractivity value of region 90. Also, region 94 is nearer toaircraft B than region 90 is to aircraft A. Refraction of GNSS signalpath 94 results in GNSS signal path 99 at aircraft B. In this example,the actual arrival angle 89 of the GNSS signal path at aircraft B isgreater than the actual arrival angle 88 of the GNSS signal path 96 ataircraft A, but the GNSS signal path 97 and 99 arrive with the sameabsolute phase at both aircraft A and aircraft B, respectively.

Another example of ambiguity due to vertical non-homogeneity isillustrated in FIG. 4. In FIG. 4, the GNSS path 100 traverses a firstconvex region 102 characterized by a first refractivity value, N₁, andthrough a second convex region 104 characterized by high refractivityvalue, N₀, wherein N₁>N₀. Region 108 is smaller than region 102, butnearer to aircraft B than region 102 is to aircraft A. Refraction ofGNSS signal paths 100 and 106 result in GNSS signal path 101 and 107.Thus, as shown in the drawing, the arrival angles 95 and 103 of the GNSSsignal paths 101 and 107 are identical. Although the refractivity of theregions differ, the distance from the region the signal must travel tothe aircraft is also different. The absolute phase delay of the GNSSsignal path 101 at aircraft A is greater than the absolute phase delayof the GNSS signal path 107 at aircraft B because of the longer distancethe signal must travel to reach the aircraft. While these figures showsimple illustrations of the more complex, actual atmospheric principles,the combined measurement of phase and angle is helpful in reducingvertical ambiguity, and results in greater weather prediction accuracy.

More than one computational method is known for transforming themeasurements of the arrival angle of the signal and the measurements ofthe absolute phase angle of the signal into estimated atmosphericprofiles. One method that is generally considered the most versatile andmost accepted in the meteorology community is based on variationalanalysis. In this method, commonly referred to as 3Dvar, a vector x,contains values of atmospheric properties to be estimated. The vector xmay include values pertaining to variables such as temperature orhumidity at various latitude/longitude/altitude locations in the Earth'satmosphere. The values in vector x are varied to minimize a costfunction given by Equation 3, as follows:J(x)=½(x−x _(b))^(T) B ⁻¹(x−x _(b))+½(Hx−y ₀)^(T) R ⁻¹(Hx−y ₀)  Equation3

where:

-   -   x=Vector of atmospheric properties to be estimated    -   J(x)=Cost function to be minimized    -   T=Matrix transposition operator x_(b)=prior estimate of x based        on other models    -   B=Matrix of weights based on confidence in and covariance of        various values in x_(b)    -   H=Forward model that transforms a given vector of atmospheric        properties into a vector of quantities actually observed    -   R=Matrix of weights based on confidence in and covariance of        various values of Hx and y₀    -   y₀=Vector of observations including one or more measurements of        refractive bending angles and one or more measurements of        absolute phase.

It should be noted that the forward model H used in each case depends onthe trajectories of the airplane and of the GNSS satellite used for theoccultation measurements. In addition, the same equation can be utilizedto transform the actual arrival angle of the GNSS signal into profilesof physical properties of the atmosphere, where the variables representslightly different elements as follows:J(x)=½(x−x _(b))^(T) B ⁻¹(x−x _(b))+½(Hx−y ₀)^(T) R ⁻¹(Hx−y ₀)  Equation3B

where: x=Vector of atmospheric properties to be estimated

-   -   J(x)=Cost function to be minimized    -   T=Matrix transposition operator    -   x_(b)=prior estimate of x based on other models    -   B=Matrix of weights based on confidence in and covariance of        various values in x_(b)    -   H=Forward model that transforms a given vector of atmospheric        properties into a vector of quantities actually observed    -   R=Matrix of weights based on confidence in and covariance of        various values of Hx and y₀    -   y₀=Vector of observations including one or more measurements of        refractive bending angle

The present invention includes the use of phased-array antennas capableof receiving GNSS frequencies, which are well known in the art. Onecommonly known phased-array antenna is a mobile phased array GNSSreceiver manufactured by the NAVSYS Corporation of Colorado Springs,Colo., also referred to as the High-gain Advanced GNSS Receiver (HAGR).The HAGR allows antenna elements to be placed at arbitrary locationswithin reach of a coaxial cable. The HAGR apparatus may be used topractice the present invention, to accept inputs from antenna elementslocated on an airplane fuselage and at the top of a vertical tail of theairplane. The HAGR apparatus receives both the L1 and L2 bands of GNSSsignals, which are necessary to measure as well as subtract therefractive effects of the Earth's ionosphere on the GNSS signals. TheHAGR apparatus also provides pitch, roll, and yaw compensation so theproper phase shift is maintained among the various antenna elements. Thepitch, roll, and yaw compensation assumes that the antenna elements aremounted on a truly rigid structure with no flexibility. With respect toEquation 3, additional measurements are needed when structural bendingcan exceed a large fraction of a millimeter.

Referring now to FIGS. 5A and 5B, another embodiment of the presentinvention is shown. FIG. 5A is a front view of the system with a thirdantenna element 92 added to the two-antenna element configuration shownin FIG. 2. The third antenna element 92 is horizontally offset from theother antenna elements 50 and 52. The third antenna element 92 isconnected to the same phased array receiver 54 as antenna elements 50and 52 for processing received signals. The phased array receiver 54uses relative phase measurement from the third antenna element 92 tomeasure the horizontal arrival angle of the GNSS signal as discussed ingreater detail below with respect to FIG. 9. The horizontal distancefrom the antenna elements 50, 52 to the third antenna element 92determine the precision with which the horizontal arrival angle ismeasured. FIG. 5B illustrates the front view of the system with a thirdantenna element 92 added. FIG. 5B better illustrates the effect of thehorizontal distance 76 from the antenna elements 50, 52 to the thirdantenna element 92 on the horizontal arrival angle of the signal 48.FIG. 5B illustrates the top view of the system, where the antennaelement 52 is not readily visible because it is behind antenna element50. The phase distance 78 is greater in proportion to the horizontaldistance 76.

Referring now to FIG. 5C, two GNSS signal paths arriving at a mobileplatform are compared. A large atmospheric region 84 with refractivityproperties causes horizontal bending of the GNSS signal transmitted froma satellite to a mobile platform. In case of aircraft C, however, theGNSS path 44 similarly traverses regions 77 and 84. Regions 77 and 84have different refractivity values. Refraction of GNSS signal path 80results in GNSS signal path 83 at aircraft C with actual arrival angle82. The nominal horizontal arrival angle 80 corresponds to a straightpath from satellite to aircraft C, while the actual horizontal arrivalangle 82 depends on the location and shape of the region 84 and on itsrefractivity properties.

Referring next to FIG. 6, an exemplary method of the present inventionis set forth. As discussed above and shown in FIG. 2, a plurality ofantenna elements 50, 52 and receivers 54 are provided to implement thepresent method. The system is started at Step 109. At Step 112, thesystem simultaneously receives a GNSS signal at each of a plurality ofthe antenna elements 50, 52, after the signal passes through theatmosphere. The antenna elements 50, 52 are configured to measure thearrival angle of the signal, from which the receiver 54 determines anominal arrival angle 48 of the GNSS signal from the incoming GNSSsignal as shown in FIG. 2. The nominal arrival angle is computed fromknown positions of the satellites 14 as shown in FIG. 1, and the antennaelements 50, 52. The satellite positions are calculated from informationencoded in the GNSS signal. For non-GNSS satellites, the position iscalculated from published ephemerises. The antenna element positions arefound in any one of several ways. One way may be using GNSS informationfrom multiple satellites. The actual arrival angle 56 reveals the totalrefractive bending caused by the path of the signal through theatmosphere and any atmospheric properties 30 shown in FIG. 1 that theGNSS signal may encounter along the path. Next, at Step 113, the nominalarrival angle is computed, and at Step 114, the arrival angle of theGNSS signal is measured. The receiver measures a relative arrival angle(relative to the antenna). This relative arrival angle is transformedinto an absolute angle by adding the orientation of the antenna relativeto the geographically fixed coordinate system. After measuring thearrival angle of the GNSS signal, the system determines the differencebetween the nominal arrival angle 48 of the GNSS signal and the actualarrival angle 56 shown in FIG. 2 of GNSS signal at Step 116. Finally,the refractive bending angle between actual and nominal GNSS arrivalangle is calculated at Step 118. The relative signal offset for theplatform is then determined in step 120.

Referring next to FIG. 7, an alternate embodiment of the presentinvention is set forth. As discussed above, a plurality of antennaelements 50, 52 and receiver 54 shown in FIG. 2 are provided toimplement the present method. The system is started at Step 210. At Step212, the system simultaneously receives a GNSS signal at each of aplurality of the antenna elements 50, 52, after the signal passesthrough the atmosphere. The antenna elements 50, 52 and receiver 54 areconfigured to measure the phases of the signal, and to determine anominal arrival angle 48, shown in FIG. 2, of the GNSS signal from theincoming GNSS signal. Next, at step 213, the difference between thephases of the GNSS signal for each antenna element is determined. AtStep 214, the arrival angle of the GNSS signal is measured. Aftermeasuring the arrival angle and phase of the GNSS signal, the systemdetermines the difference between the nominal arrival angle 48 of theGNSS signal and the actual arrival angle 56 of GNSS signal and betweenthe nominal arrival phase and the actual arrival phase of GNSS signal atStep 216. Finally, the refractive bending angle of the GNSS signal iscalculated in Step 218 based on the difference between the actual 56 andnominal arrival angles 48 and the actual and nominal arrival phases ofthe GNSS signal. The relative signal offset for the platform is thendetermined in step 120.

Referring now to FIG. 8, another embodiment of the present inventionalso compensates for motion or inaccuracies caused by mobile platforms.After the steps from either of FIG. 6 or 7 are completed, Step 122 ofFIG. 8 determines if the platform, which the antenna elements arelocated on, is a mobile platform. If the platform is mobile, then thesystem proceeds in Step 124 to estimate the relative phase offset of theGNSS signal at each antenna element due to the structural rotation ofthe platform. If the platform is not mobile, the system proceedsdirectly to Step 125. In Step 125, the system determines whether a thirdantenna element is present. If a third antenna element is not present,then the system transforms the actual arrival angle of the GNSS signaland the absolute phase angle of the GNSS into atmospheric profiles instep 220. If a third antenna element is present, then the system moveson to further steps, which are discussed in FIG. 9 below.

Referring to FIG. 9, measurement of the horizontal arrival angle as wellas the vertical arrival angle and the absolute phase allows the presentinvention to estimate atmospheric variations that are horizontal andperpendicular to the GNSS path. Measurements of horizontal gradients areof great value to predictive weather models because they can be used toimprove the accuracy of vertical profiles since estimated verticalprofiles are not forced to fit a model that assumes horizontalhomogeneity. This embodiment is easily achieved when using airplanes asplatforms for mounting the antenna elements. Because airplanes have longwingspans and large fuselages, it is easy to achieve large horizontalseparations of the antenna elements by placing them far apart on theairplane. This enables very precise measurements of horizontal arrivalangles, and therefore good estimates of horizontal refractivitygradients. Once the system determines that a third antenna element ispresent in step 125, the system measures the horizontal arrival angle ofthe GNSS signal in Step 126. The difference between nominal and actualhorizontal arrival angle of the GNSS path signal is calculated in Step128, and then data is transformed into accurate atmospheric profiles inStep 130. Therefore, it is intended that the invention not be limited tothe particular embodiment disclosed as the best mode contemplated forcarrying out this invention, but that the invention will include allembodiments falling within the scope of the appended claims.

While the invention has been described with reference to a preferredembodiment, it will be understood by those skilled in the art thatvarious changes may be made and equivalents may be substituted forelements thereof without departing from the scope of the invention. Inaddition, many modifications may be made to adapt a particular situationor material to the teachings of the invention without departing from theessential scope thereof.

1. A method of determining refractivity properties of the Earth'satmosphere using Global Navigation Satellite System (GNSS) signals, themethod comprising: providing a plurality of antenna elements configuredto measure an actual arrival angle of a GNSS signal, the antennaelements mounted on a platform and separated by a predetermined verticaldistance; providing a receiver device, the receiver device being coupledto each of the plurality of antenna elements and configured to compute anominal arrival angle of the GNSS signal based on data transmitted froma source of the GNSS signal; receiving the GNSS signal at each of theplurality of antenna elements; measuring an actual arrival angle of theGNSS signal using the plurality of antenna elements; determining adifference between the nominal arrival angle of the GNSS signal and theactual arrival angle of GNSS signal; calculating a refractive bendingangle of the GNSS signal based on the determined difference between theactual and nominal GNSS arrival angles; and transforming the refractivebending angle of the GNSS signal into a profile of physical propertiesof the atmosphere.
 2. The method of claim 1, wherein the step oftransforming the refractive bending angle of the GNSS signal into aprofile of physical properties of the atmosphere, includes: defining avector, the vector including a plurality of values of atmosphericproperties to be estimated, varying at least one of the values of theplurality of values in the vector, and minimizing a cost function givenby the following equation:J(x)½(x−x _(b))^(T) B ⁻¹(x−x _(b))+½(Hx−y ₀)^(T) R ⁻¹(Hx−y ₀) where:x=vector of atmospheric properties to be estimated; J(x)=Cost functionto be minimized; T=Matrix transposition operator; x_(b)=prior estimateof x based on other models; B=Matrix of weights based on confidence inand covariance of various values in x_(b); H=Forward model thattransforms a given vector of atmospheric properties into a vector ofquantities actually observed; R=Matrix of weighs based on confidence inand covariance of various values of Hx and y₀; y₀=vector of observationsincluding one or more measurements of refractive bending angles.
 3. Themethod of claim 1, wherein the plurality of antenna elements comprisesat least one high-gain steerable dish antenna elements.
 4. The method ofclaim 3, wherein the platform is a mobile platform and the method alsoincludes estimating a relative arrival angle offset due to structuralflexing of the platform of the GNSS signal at each of the plurality ofantenna elements.
 5. The method of claim 3, wherein the platform is amobile platform, and the method also includes estimating a relativeoffset angle of the GNSS signal for each high-gain steerable dishantenna of the plurality of antenna elements due to structural rotationof the platform.
 6. The method of claim 1, wherein the plurality ofantenna elements comprises a vertical phased array of two or more GNSSantenna elements.
 7. The method of claim 6, wherein the method alsoincludes estimating a relative phase offset due to structural flexing ofthe platform of the GNSS signal at each of the plurality of antennaelements.
 8. The method of claim 7 wherein the method includesinstalling an inertial measurement unit (IMU) proximate to each antennaelement of the plurality of antenna elements, and measuring structuralflexing of the platform.
 9. The method of claim 8, wherein a pluralityof IMUs are configured to compensate for flexing or mobility of themobile platform.
 10. The method of claim 8, wherein the at least one IMUis provided for each antenna element of the plurality of antennaelements, each IMU being disposed proximately to the correspondingantenna element.
 11. The method of claim 6, wherein the receiver is alsoconfigured to measure the phase difference between GNSS signals arrivingat each of the plurality of antenna elements.
 12. The method of claim11, wherein the method also includes: providing an additional antennaelement, the additional antenna element being horizontally separatedfrom the plurality of antenna elements and connected to the receiverunit, the receiver unit also being configured to measure a horizontalangle of the GNSS signal; and estimating atmospheric variations that arehorizontal and perpendicular to the GNSS path.
 13. The method of claim11, wherein the method includes providing at least one IMU forestimating a relative phase shift between the antenna elements.
 14. Themethod of claim 13, wherein the at least one IMU includes a first IMUconfigured to compensate for rotation and motion of the mobile platform.15. A method of determining refractivity properties of the Earth'satmosphere using Global Navigation Satellite System (GNSS) signals, themethod comprising: providing a plurality of antenna elements configuredto measure an actual arrival angle and actual arrival phase of a GNSSsignal, the antenna elements mounted on a platform and separated by apredetermined vertical distance; providing a receiver device, thereceiver device being coupled to each of the plurality of antennaelements and configured to calculate a nominal arrival angle and anominal arrival phase of the GNSS signal based on data transmitted froma source of the GNSS signal; receiving the GNSS signal at each of theplurality of antenna elements; measuring an actual arrival angle of theGNSS signal; measuring an actual arrival phase of the GNSS signal foreach antenna element of the plurality of antenna elements; determining adifference between the nominal arrival angle of the GNSS signal and theactual arrival angle of GNSS signal; determining a difference betweenthe nominal arrival phase of the GNSS signal and the actual arrivalphase of GNSS signal; calculating a refractive bending angle and anabsolute phase shift of the GNSS signal based on the determineddifferences between the actual and nominal arrival angles of the GNSSsignal and the actual and nominal arrival phases of the GNSS signal; andgenerating a profile of physical properties of the atmosphere based on atransformation of the refractive bending angle of the GNSS signal andthe absolute phase shift of the GNSS signal.
 16. The method of claim 15,wherein the step of generating a profile of physical properties of theatmosphere based on a transformation includes: defining a vector, thevector including a plurality of values of atmospheric properties to beestimated, varying at least one of the values of the plurality of valuesin the vector, and minimizing a cost function given by the followingequation:J(x)=½(x−x _(b))^(T) B ⁻¹(x−x _(b))+½(Hx−y ₀)^(T) R ⁻¹(Hx−y ₀) where:x=vector of atmospheric properties to be estimated; J(x)=Cost functionto be minimized; T=Matrix transposition operator; x_(b)=prior estimateof x based on other models; B=Matrix of weights based on confidence inand covariance of various values in x_(b); H=Forward model thattransforms a given vector of atmospheric properties into a vector ofquantities actually observed; R=Matrix of weighs based on confidence inand covariance of various values of Hx and y₀; y₀=vector of observationsincluding one or more measurements of refractive bending angles and oneor more measurements of absolute phase.
 17. The method of claim 15 alsocomprising: providing means for estimating a relative phase shift of theGNSS signal due to structural movement of the platform, for each of theplurality of antenna elements; before calculating the refractive bendingangle, computing a relative phase shift associated with structuralmotion; and subtracting from the phase of the GNSS signal the relativephase shift.
 18. A system for determining refractivity properties of theEarth's atmosphere using Global Navigation Satellite System (GNSS)signals comprising: a plurality of antenna elements configured tomeasure the arrival angle of a GNSS signal, the plurality of antennaelements mounted on a platform and separated by a predetermined verticaldistance; a receiver unit, the receiver unit being coupled to each ofthe plurality of antenna elements; wherein the receiver unit beingconfigured to: receive the GNSS signal detected by each of the pluralityof antenna elements; measure an actual arrival phase of the GNSS signalfor each antenna element of the plurality of antenna elements; computean actual arrival angle from the arrival phases; determine a differencebetween the nominal arrival angle of the GNSS signal and the actualarrival angle of GNSS signal; calculate a refractive bending angle ofthe GNSS signal based on the determined differences between the actualand nominal arrival angles of the GNSS signal; and generate a profile ofphysical properties of the atmosphere based on a transformation of therefractive bending angle of the GNSS signal.
 19. The system of claim 18,wherein the plurality of antenna elements comprises a vertical phasedarray of two or more GNSS antenna elements.
 20. The system of claim 19,wherein the system also includes an additional antenna element, theadditional antenna element being horizontally separated from theplurality of antenna elements and connected to a receiver unit, thereceiver unit also being configured to measure a horizontal angle of theGNSS signal, wherein the additional antenna elements are used to computeatmospheric variations that are horizontal and perpendicular to a GNSSsignal path.
 21. The system of claim 18, wherein the plurality ofantenna elements comprises at least one high-gain steerable dish antennaelements.
 22. The system of claim 18, wherein the platform is a mobileplatform, and the system also includes a means for estimating a relativephase shift of the GNSS signal due to structural movement of theplatform, for each the plurality of antenna elements.
 23. The system ofclaim 18, wherein the means for estimating a relative phase shiftbetween the antenna elements comprises at least one inertial measurementunit.
 24. The system of claim 23, wherein the at least one inertialmeasurement units includes a first IMU configured to compensate forrotation and motion of the mobile platform, and additional IMUs areconfigured to compensate for flexing or mobility of the mobile platform.25. The system of claim 24, wherein the at least one IMU is provided foreach antenna element of the plurality of antenna elements, each IMUbeing disposed proximately to the corresponding antenna element.
 26. Thesystem of claim 18 wherein the receiver unit is further configured to:determine a difference between the nominal arrival phase of the GNSSsignal and the actual arrival phase of the GNSS signal; calculate anabsolute phase shift of the GNSS signal based on the determineddifference between the actual and nominal arrival phases of the GNSSsignal; and generate a profile of physical properties of the atmospherebased on a transformation of the refractive bending angle of the GNSSsignal and the absolute phase shift of the GNSS signal.